# If I were close to the speed of light and throw a ball...

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## Main Question or Discussion Point

If I were of speed 299 792 457 m/s relative to an observer and throw a ball, what would the observer see?

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The observer would see the ball go very fast, with velocity $v= \frac{u+w}{1+\frac{uw}{c^2}}$ where $u$ and $w$ are yours and the ball's speed respectively.

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The observer would see the ball go very fast, with velocity $v= \frac{u+w}{1+\frac{uw}{c^2}}$ where $u$ and $w$ are yours and the ball's speed respectively.
....where $u$ is your speed relative to the observer and $w$ is the speed at which you throw the ball relative to you.
You can simplify the formula a bit by choosing to measure time in seconds and distances in light-seconds so $c=1$ (light-second per second), dividing by $c^2$ is just dividing by one so we can ignore it, and the formula becomes $v=\frac{u+w}{1+uw}$.

It's an interesting exercise to consider what would happen if you were shining a light straight ahead - we'd set $w$ to $c$ because that's the speed of the light beam relative to you. What is its speed relative to the observer?

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